Estimating noise at one frequency by sampling noise at other frequencies

ABSTRACT

A method, apparatus and computer program for improving the signal-to-noise ratio of a signal S(t), S(t) containing Signal and noise, are disclosed. A measurement of S(t) at a frequency-of-interest is obtained. Noise measurements of S(t) at one or more noise frequencies where the Signal portion of S(t) is expected to be small are obtained. The noise at the frequency-of-interest is estimated using the noise measurements at the one or more noise frequencies. The estimated noise is subtracted from the measurement of S(t) at the frequency-of-interest.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.11/793,121 filed Jun. 14, 2007, now U.S. Pat. No. 7,593,815 which is theNational Stage of International Application No. PCT/US2006/01555, filed17 Jan. 2006 which claims the benefit of U.S. Provisional ApplicationNo. 60/653,427 filed on Feb. 16, 2005 and U.S. Provisional ApplicationNo. 60/654,595 filed on Feb. 18, 2005, hereby incorporated by reference.

BACKGROUND

Electromagnetic soundings, including controlled source electromagnetic(“CSEM”) experiments, are conducted by transmitting an electromagneticsignal, typically a low-frequency periodic waveform, into thesubsurface, and measuring the electromagnetic response. U.S. Pat. No.6,603,313 to Srnka and U.S. Patent Publication No. 2003/0050759 (PCTPublication No. WO 03/025803) by Srnka and Carazzone disclose methodsfor using CSEM measurements to prospect for oil and gas, and todelineate known prospects.

As illustrated in FIG. 1, which shows an example of the equipmentinvolved in performing a marine CSEM survey, one end of an antenna 105is attached to a tow body 110, which is lowered to the desired waterdepth via a sub-sea tow cable 115. The tow body 110 is more than just ananchor point for the tow cable. It provides a place to contain theelectrical components necessary for generating an electromagnetic sourcewave, and also may contain communication systems, positioning systems,speed of sound measuring devices, altimeters and the like, that areuseful in surveying. A winch (not shown), attached to a surface vessel120, controls the tow cable 115.

The antenna 105 is the transducer of electromagnetic fields used for theCSEM survey. Marine CSEM surveys typically use horizontal electricdipoles (HED) which may be made as follows. Two insulated wires areextended from two output terminals of a power generator capable ofsupplying electrical power with a desired frequency and waveform. Theother end of each insulated wire is connected to an electrode.Alternatively, the insulation may be stripped from the end of theinsulated wire and the bare wire becomes the electrode. The twoelectrodes are maintained a fixed distance apart. The dipole axis ismaintained in a horizontal posture in the case of an HED. A current loopbetween the two electrodes is completed in a marine application by thewater, the sea bottom, and possibly the air above the water.

The antenna 105 generates a time-varying electromagnetic field 130which, in the example shown in FIG. 1, penetrates the sea bottom 125 toa formation 135. The time-varying electromagnetic field causes atime-varying current 140 to flow in the formation 135. The flow of thetime-varying current 140 through the formation 135 induces anotherelectromagnetic field 145. An array of sensors 150, typically located onthe sea floor, receives, detects, and analyzes the electromagnetic field145, and stores the resulting data or reports it to the surface foranalysis. The characteristics of the received electromagnetic field 145depend on the characteristics of the transmitted electromagnetic field130, which are known to some degree, the characteristics of theformation 135, the characteristics of other subsurface features andformations, and noise. It is possible to determine some of thecharacteristics of the formation 135 by analyzing the receivedelectromagnetic field 145 in this context.

A typical sensor 150, illustrated in FIG. 2, includes an electronicspackage 205 coupled to a ballast 210. The electronics package 205includes four antennae 215 arranged approximately symmetrically aroundits periphery. The four antennae form two electric dipoles, as describedabove. One or more vertical antennae (not shown) may also be included todetect vertically oriented electromagnetic radiation. The antennae 215receive the electromagnetic field 145 and equipment in the electronicspackage 205 detect, analyze and record data related to the phase andamplitude of the electromagnetic field 145. When sufficient data hasbeen recorded or after a certain period of time has passed, theelectronics package 205 releases from the ballast 210 and floats to thesurface where it is recovered. On the surface, data is recovered fromthe electronics package 205. The data are analyzed.

A survey is composed of the data collected as the result of one or moretraverses of the antenna 105 over an area of the seafloor containing oneor more sensors 150. Typically, each of the traverses is known as a“towline.”

One of the most significant sources of noise for the CSEM application ismagnetotelluric noise 155, shown on FIG. 1 as a set of arrowed lines. Inaddition, noise may stem from seafloor oceanic currents triggeringmechanical vibration of the antennae (“strum”) or from imperfections inthe sensor electronics.

SUMMARY

In general, in one aspect the invention features a method for improvingthe signal-to-noise ratio of a signal S(t), S(t) containing Signal andnoise. The method includes (a) obtaining a measurement of S(t) at afrequency-of-interest, (b) obtaining noise measurements of S(t) at oneor more noise frequencies where the Signal portion of S(t) is expectedto be small, (c) estimating the noise at the frequency-of-interest usingthe noise measurements at the one or more noise frequencies, and (d)subtracting the estimated noise from the measurement of S(t) at thefrequency-of-interest.

Implementations of the invention may include one or more of thefollowing. The method may further include repeating (a), (b), (c) and(d). Estimating the noise at the frequency-of-interest, N(T), mayinclude minimizing

$\sum\limits_{T \in {\{{T_{1}T_{2}}\}}}{{{S(T)} - {N(T)}}}^{2}$where N(T)=c₁n₁(T)+c₂n₂(T)+c₃n₃(T)+ . . . ; and where c₁, c₂, c₃, . . .are complex coefficients; n₁, n₂, n₃, . . . are the measurements ofnoise at the noise frequencies; and T1 and T2 define a time period whenlittle or no Signal is present in S(t). Obtaining noise measurements ofS(t) at the one or more noise frequencies may include selecting thenoise frequencies such that they will readily model the noise at thefrequency-of-interest. Obtaining noise measurements of S(t) at the oneor more noise frequencies may include selecting the noise frequencies tobe close to the frequency-of-interest. Obtaining noise measurements ofS(t) at the one or more noise frequencies may include obtainingmeasurements of S(t) at a time when the Signal portion of S(t) isexpected to be small. The measurements may include data. The data mayinclude offset, amplitude and phase. Estimating the noise may includesorting the data into bins, each bin being associated with a respectiverange of offsets; transforming the data in each bin into the frequencydomain; selecting from each bin data associated with thefrequency-of-interest; selecting from each bin data associated with theone or more noise frequencies; estimating, for each bin, afrequency-of-interest noise from the selected noise frequency data; andsubtracting, on a bin-by-bin basis, the estimated frequency-of-interestnoise from the data associated with the frequency-of-interest. Obtaininga measurement of S(t) at the frequency-of-interest may include obtainingmeasurements of the complex amplitude of S(t) at thefrequency-of-interest. Obtaining noise measurements of S(t) at the oneor more noise frequencies may include obtaining measurements of thecomplex amplitude of S(t) at the one or more noise frequencies.Estimating the noise may include estimating the complex amplitude of thenoise at the frequency-of-interest using the complex amplitudes of S(t)obtained at the one or more noise frequencies. Subtracting the estimatednoise may include subtracting the complex amplitude of the estimatednoise at the frequency-of-interest from the complex amplitude of S(t)obtained at the frequency-of-interest.

It should be noted that the time variable t in S(t) refers to time as ameasure of source position relative to receiver position. This is notthe time variable that is converted to frequency when the data in eachbin are transformed to the frequency domain. The Fourier-transformedtime variable is, for example, the time variable represented on thehorizontal axis of FIG. 5, whereas the time variable in S(t) denotes thetime at the bin centers after spectral decomposition (transformation tothe frequency domain).

The method may include generating a CSEM signal having a large amount ofenergy at the frequency-of-interest and small amount of energy at aplurality of low-signal frequencies. The method may further includetransmitting the CSEM signal and receiving the signal S(t). The methodmay further include selecting a frequency for the CSEM signal.Generating the CSEM signal may include generating a CSEM signal in whichthe energy of the CSEM signal is concentrated into temporal frequenciessuited to distinguish hydrocarbon reservoirs. The method may furtherinclude selecting the noise frequencies to coincide with a subset of thelow-signal frequencies. The method may further include selecting thenoise frequencies to avoid frequency components of the transmitted CSEMsignal. Generating a CSEM signal may include generating a square wave.Generating a CSEM signal may include generating a tripeak wave.

In general, in another aspect, the invention features a computerprogram, stored in a tangible medium, for improving the signal-to-noiseratio of a signal S(t), S(t) containing Signal and noise. The programincludes executable instructions that cause a computer to (a) obtain ameasurement of S(t) at a frequency-of-interest; (b) obtain noisemeasurements of S(t) at a plurality of noise frequencies where theSignal portion of S(t) is expected to be small; (c) estimate the noiseat the frequency-of-interest using the noise measurements at the one ormore noise frequencies; and (d) subtract the estimated noise from themeasurement of S(t) at the frequency-of-interest.

In general, in another aspect, the invention features a CSEM apparatusfor estimating noise at one frequency in a signal S(t), which containsSignal and noise, by sampling noise in S(t) at other frequencies. Theapparatus includes a noise estimator to determine an estimate of thenoise in S(t) at a frequency-of-interest using the measured noise inS(t) at certain noise frequencies and a noise subtractor to subtract theestimate of noise from S(t) at the frequency-of-interest.

Implementations of the invention may include one or more of thefollowing. The CSEM apparatus may further include one or more antennae;one or more analog to digital converters coupled to the antennae, eachproducing data representing S(t); and a data transformer to transformthe data from the time domain to the frequency domain. The CSEMapparatus may further include a recorder coupled to the analog todigital converter, the recorder recording the output of the analog todigital converter. The CSEM apparatus may further include a data binnercoupled to the analog to digital converter to sort its output into binsbased on offset. The CSEM apparatus may further include conditioningcomponents coupled to the antennae. The noise estimator may minimize

$\sum\limits_{T \in {\{{T_{1}T_{2}}\}}}{{{S(T)} - {N(T)}}}^{2}$where N(T)=c₁n₁(T)+c₂n₂(T)+c₃n₃(T)+ . . . ; c₁, c₂, c₃, . . . arecomplex coefficients; n₁, n₂, n₃, . . . are the measurements of noise atthe noise frequencies; and T1 and T2 define a time period when little orno Signal is present in S(t). The noise estimator may estimate the noisereceived on a single antenna. The noise estimator may estimate the noisereceived on two or more antennae.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the operating environment for a CSEM survey.

FIG. 2 illustrates a CSEM survey sensor.

FIG. 3 is a block diagram of a transmitter for use in a CSEM survey.

FIG. 4 is a block diagram of a device to receive and process CSEM data.

FIG. 5 illustrates an ideal square wave.

FIG. 6 illustrates an ideal tripeak wave.

FIG. 7 shows a portion of the spectrum of an ideal square wave.

FIG. 8 shows a portion of the spectrum of an ideal tripeak wave.

FIG. 9 illustrates a segment of a practical high-power square wave.

FIG. 10 is a flow chart depicting a technique for increasing the signalto noise ratio in CSEM data.

FIGS. 11-15 illustrate an example of the improvement in signal-to-noiseratio produced by practicing the technique described herein.

DETAILED DESCRIPTION

To avoid confusion, the word Signal, when capitalized, refers to thesignal component of a signal (uncapitalized) that includes both Signaland noise. A CSEM system increases the signal-to-noise ratio of CSEMdata by transmitting a CSEM electromagnetic signal that has known gapsin its spectrum; receiving a CSEM electromagnetic signal that in alinear noiseless environment would be expected to have the same spectralcontent as the transmitted CSEM electromagnetic signal; using the noisereceived in the known gaps to estimate the noise atfrequencies-of-interest where Signal is expected to be found; andsubtracting the estimated noise from the received CSEM electromagneticsignal at the frequencies-of-interest.

An example of apparatus to generate the transmitted CSEM electromagneticsignal 130, which is typically located in the tow body 110, isillustrated in FIG. 3. It includes a waveform generator 305 thatgenerates a waveform having desired characteristics. The waveformgenerator 305 is coupled to a CSEM transmitter 310, which transmits thegenerated waveform through the antenna 105 and creates the transmittedelectromagnetic field 130.

In a typical CSEM application, the waveform is selected to concentratethe available transmitter power into a few selected temporalfrequencies, which are chosen to best distinguish hydrocarbon reservoirsin the subsurface. The transmitter current takes a form that repeats intime, such as the square wave shown in FIG. 5. or the tripeak waveformshown in FIG. 6. The tripeak waveform shown in FIG. 6 is of the typedisclosed in PCT International Patent Publication Number WO2005/117326entitled Logarithmic Spectrum Transmitter Waveform for Controlled-SourceElectromagnetic Surveying, by Lu and Srnka, published on 8 Dec. 2005.

It is well known from the theory of Fourier Analysis that non-sinusoidalwaveforms such as those shown in FIGS. 5 and 6 are equivalent to a sumof sinusoidal waveforms, each representing a specific temporalfrequency. After Fourier Analysis, the amplitude of each sinusoidrepresents the relative contribution of its frequency to thenon-sinusoidal waveform. The lowest such frequency generally correspondsto the period over which the waveform repeats. For example, if thesymmetric 8-second square wave shown in FIG. 5 is repeated, theresulting continuous waveform is composed of frequencies (2*N+1)/8 Hz,where N=0, 1, 2, . . . , or 1/8, 3/8, 5/8 Hz, etc. These frequencies andthe amplitude of the signal at each of these frequencies are illustratedin FIG. 7. The following tables 1 and 2 describe a continuous squarewave and its first few frequency components, where T is the period ofthe square wave (e.g., 8 seconds in FIG. 5):

TABLE 1 Square Wave Transitions Transition Time 1 to −1 T/2 −1 to 1 T

TABLE 2 First Few Frequency Components of a Symmetric Square WaveFrequency Amplitude Phase  1/T 1.2732 0.0  3/T 0.4244 0.0  5/T 0.25460.0  7/T 0.1819 0.0  9/T 0.1415 0.0 11/T 0.1157 0.0 13/T 0.0979 0.0 15/T0.0849 0.0 17/T 0.0749 0.0 19/T 0.0670 0.0 21/T 0.0606 0.0

Tables 3 and 4 below describe a continuous tripeak waveform and itsfirst few frequency components, where T is the period of the tripeakwaveform. These frequencies and the amplitude of the signal at each ofthese frequencies are illustrated in FIG. 8.

TABLE 3 Tripeak Wave Transitions Transition Time −1 to 1  18*T/256 1 to0  60*T/256 0 to 1  67*T/256 1 to −1 110*T/256 −1 to 0 147*T/256 0 to −1186*T/256 −1 to 0 198*T/256 0 to −1 237*T/256

TABLE 4 First Few Frequency Components of Tripeak Wave FrequencyAmplitude Phase  1/T 0.6212 0.0  2/T 0.6010 −90.0  4/T 0.6064 −90.0  7/T0.1183 180.0 10/T 0.2966 90.0 14/T 0.0801 90.0 16/T 0.1596 −90.0 20/T0.0756 −90.0

Practical high power transmitters do not generate ideal square waves asshown in FIG. 5 or ideal tripeak waves as shown in FIG. 6. They generatemore complex waveforms, such as that shown in FIG. 9, in which thepositive excursions are composed of positive lobes of a rectifiedalternating current and the negative excursions are composed of negativelobes of the rectified alternating current. The frequency content ofsuch complex waveforms will not have the clean spectrum shown in FIGS. 7and 8.

An example of apparatus to detect and process the received CSEMelectromagnetic signal 145, illustrated in FIG. 4, includes the antennae215. The antennae 215 are coupled to amplifiers and conditioners 405,which amplify and condition the signal from the antennae. Conditioningmay include filtering, attenuating, or delaying part or all of thereceived signal. The amplifiers and conditioners 405 are coupled to ananalog to digital (A/D) converter 410 which converts the analog signalto a digital representation. The A/D converter has a wide enoughbandwidth and dynamic range to record the signal for analysis.Particularly for the signal-to-noise improvement apparatus describedherein, the A/D converter has sufficient bandwidth to capture thefrequencies where little or no Signal is expected, as described below.An example A/D converter operates at 31.125 Hz and provides a 24-bitoutput. Another example A/D converter operates at 50 Hz.

As can be seen from Table 4 and FIG. 8, much of the energy in a tripeakwaveform with an 8-second period is at discrete frequencies 1/8 Hz, 2/8Hz, and 4/8 Hz. By contrast, the A/D converter samples at a much finertime interval, such as 0.032 seconds, allowing the A/D converter toreliably capture frequencies from 0 Hz (direct current) to the Nyquistcutoff frequency at 15.625 Hz. As a result, the data output from the A/Dconverter contains many frequencies other than those transmitted. Forexample, in the case of tripeak wave with an 8-second period (T=8), theoutput of an A/D converter sampling at 0.032 second intervals wouldcontain, not just the frequencies-of-interest shown in Table 4 (i.e.,1/8, 2/8, 4/8, 7/8, 10/8, 14/8, and 20/8 Hz), but also 3/8, 5/8, 6/8,etc. Hz. where only noise energy is expected to be found.

Turning back to FIG. 4, the output of the analog to digital converter410 is optionally coupled to a recorder 415, which records the digitaldata for later processing. In some configurations the recorder 415 isnot used. In some configurations, the data is analyzed in real time.

The recorded data are then provided to a data binner 420. The databinner 420 extracts a time segment of recorded data corresponding to atowline and divides that segment into bins. Each bin is associated withan interval of time ranging generally between 2 and 128 seconds. In thecase of a moving source, that time interval may correspond to a range ofoffsets that range generally falling between 50 and 600 meters. Offsetis defined to be the signed distance, which is sometimes expressed astime and sometimes as a physical distance, from the antenna 105 to thesensor 150 that received the data being binned. Thus, each towline hasassociated with it a set of bins, each of which contains a time segmentof data from that towline.

The data in each bin are then transformed by a data transformer 425 fromthe time domain into the frequency domain. The data transformer 425 alsocollects the resulting complex amplitude data (i.e., amplitude andphase) from all of the bins for one or more frequencies to be used insubsequent analysis. For example, the data transformer 425 may collectthe 1/8 Hz amplitude and phase data from each of the bins. The resultwould be a data collection such as that shown in FIG. 11. As can beseen, FIG. 11 has two charts for data collected at 1/16 Hz. Both chartshave offset measured in Julian days as the horizontal axis. In onechart, the vertical axis is the amplitude of energy at the correspondingoffset on the horizontal axis at 1/16 Hz. In the other chart, thevertical axis is related to the phase of energy at the correspondingoffset on the horizontal axis at 1/16 Hz. Each individual point in thecurves shown in the two charts in FIG. 11 corresponds to the data in asingle bin.

The data collected by the data transformer 425 are provided to a noiseestimator 430. The noise estimator estimates the noise at frequencieswhere Signal power is expected using the noise collected at frequencieswhere no Signal power is expected. For example, using the spectrumillustrated in FIG. 7 as an example, the noise at 1/8, 3/8 and 5/8 Hzmay be estimated using the noise measured at 1/16, 3/16, 1/4, and 1/2Hz.

In one example system, the noise at a Signal frequency (such as 1/8 Hzin FIG. 7) is modeled by a linear combination of the data at the noisefrequencies (such as 1/16, 3/16, 1/4 and 1/2 Hz in FIG. 7). That is, themodeled noise N at any signal frequency and bin time T is given by:N(T)=c ₁ n ₁(T)+c ₂ n ₂(T)+c ₃ n ₃(T)+ . . .   (1)where c₁, c₂, . . . are complex coefficients and n₁, n₂, . . . arerecorded data at the selected noise frequencies. The c_(i) aredetermined by minimizing in a least-squares sense, the differencebetween the recorded signal S(t) and the modeled noise over a timeperiod when the source is either inactive or distant enough from thereceiver to contribute little recorded Signal. In other words, the c_(i)are determined by minimizing:

$\begin{matrix}{\sum\limits_{T \in {\{{T_{1},T_{2}}\}}}{{{S(T)} - {N(T)}}}^{2}} & (2)\end{matrix}$where {T1, T2} is a time period when little or no Signal is present andthe square is understood to refer to the complex magnitude. The timewindow {T1, T2} is typically chosen using some measure of how well thenoise N can be modeled from the n_(i). In one example system, the timewindow is chosen when the signal at the frequencies-of-interest and atthe noise frequencies are generally in phase and the Signal is weak.

Care should be taken in choosing the noise frequencies n_(i) that weaklybut intentionally transmitted frequencies are not inadvertentlyconsidered noise. In particular, the tripeak waveform shown in FIG. 6contains some harmonics that are generally considered weak, but arestrong enough to distort the noise estimate if they are included in thenoise estimation process. In particular, an 8-second tripeak waveformwill contain very strong Signals at 1/8, 2/8 and 4/8 Hz. It will containnoticeable Signal at 7/8, 10/8, 14/8 and 16/8 Hz and other harmonics.Strong and noticeable Signal are indicated in FIG. 8 by solid circles.Still other, weaker harmonics (3/8, 5/8, 9/8, 12/8, 13/8, . . . Hz)might be considered too weak to provide useful signal but may be strongenough to corrupt a noise estimate if they are included in thecalculation. Such weaker and noise-level Signal are indicated in FIG. 8by open circles. Knowledge of the transmitter waveform and its spectrumwill serve as a clear guide to the choice of noise frequencies. Forexample, given the transmitter spectrum shown in FIG. 8 for an 8-secondtripeak waveform, the noise estimator 430 might choose frequencies 41/16and 43/16 Hz, where no Signal is expected, to estimate the noise at 21/8Hz, where Signal is expected.

This technique can be applied independently to measurements recorded bydifferent antenna 215 on a CSEM sensor 150. Alternatively, the techniquecan be applied to any combination of data from different antennae. Inparticular, it may be applied to a linear combination of measurementsintended to provide the component of the electromagnetic field collinearto or perpendicular to the transmitter antenna. To best addressinstrument noise, the method would be applied independently to differentrecording channels within the CSEM sensor 150. A recording channel 402may include a single antenna 215, a set of amplifiers and conditioners405, a A/D converter 410, and a recorder 415. Alternatively, each of theantennae 215 may be multiplexed to the same amplifiers/conditioner 405,A/D converter 410, and recorder 415. An electronics package 205 mayinclude one or more recording channels.

This technique can be applied more than once to the same data, as in acase where it is first applied to suppress magnetotelluric noise andthen applied a second time to suppress noise from antenna strum.

This technique can be applied to either land or marine CSEM surveys.

In one example system, the noise frequencies will be chosen to be closeenough to the frequency-of-interest to effectively model the noise atthe frequency-of-interest. The best choice of noise frequencies willvary from data set to data set depending on the spectral content andother characteristics of the noise.

It will be apparent to those skilled in the art that the noiseestimation model can be generalized from the linear model discussedabove to include other mathematical operators. In particular, aconvolution or filter could be applied to data values in some range oftime to estimate the noise at a single time. Alternatively, the leastsquares method could be generalized to other mathematical optimizationtechniques, the time window used to design the coefficients could begeneralized to include two or more time windows, or the c_(i)coefficients could be generalized to include a linear time trend, as inc_(i)+d_(i)*T.

Returning to FIG. 4, once the noise is estimated by the noise estimator430, the noise estimates are provided to a noise subtractor 435, whichsubtracts the estimated noise from the signal to produce an estimate ofthe Signal.

In an example of use, illustrated in FIG. 10, a CSEM system acquiresCSEM data (block 1005). As discussed above, acquiring CSEM data involvesreceiving a received CSEM signal induced by a transmitted CSEM signal,where the transmitted CSEM signal has a known waveform with knownamounts of energy at frequencies of interest and little or no energy atother frequencies. In a linear, noiseless environment, it would beexpected that the received CSEM signal would have the same frequencycontent as the transmitted CSEM signal. Practically, the received CSEMsignal contains both Signal and noise. The received CSEM signal issampled with sufficient granularity (i.e., sample rate and dynamicrange) to capture the frequencies-of-interest and the frequencies wherelittle or no Signal is expected to be found.

The CSEM system then selects at least one signal frequency (block 1010).The signal frequencies are selected from among thefrequencies-of-interest in the transmitted waveform. In most cases,fewer than all of the frequencies-of-interest will be selected.

The CSEM system then identifies one or more noise frequencies (block1015). The noise frequencies are selected from among the frequencieswhere little or no energy was transmitted in the transmitted waveform.In most cases, fewer than all of the frequencies with little or noenergy in the transmitted waveform will be selected.

The CSEM system then measures the energy at the selected noise frequencyor frequencies at an offset where the noise at thefrequencies-of-interest can readily be estimated from the noise at thenoise frequencies, such as where the phase of the noise at the noisefrequencies is likely to be close to the phase of the noise at thefrequencies of interest. The CSEM system uses those measurements toestimate the noise energy at the selected signal frequencies (block1020). For example, the estimating technique described above could beused.

The CSEM system then subtracts the estimated noise from the measuredsignal at the frequencies-of-interest (block 1025) to arrive at anestimate of the Signal at the frequencies-of-interest. In one examplesystem, the subtraction is performed on a bin-by-bin basis.

An example illustrating the operation of the technique described aboveis shown in FIGS. 11-15. In the example, a practical signal having thetripeak waveform shown in FIG. 6 with T=8 was transmitted. The originalCSEM data is shown in FIG. 11. As mentioned above, FIG. 11 includes twocharts: a chart reflecting the amplitude of the CSEM data (FIG. 11A) anda chart reflecting the phase of the CSEM data (FIG. 11B). The horizontalaxis of both charts is offset measured in time, and specifically inJulian date. The Julian date ranges from about 184.4 to about 185.3,which is when the data was collected. In other analyses, offset might bemeasured by distance.

The vertical axis of the amplitude chart in FIG. 11A is the amplitude ofthe collected data in volts per meter measured at 0.0625 Hz, which isone of the frequencies of interest in the transmitted waveform of thisexample. The vertical axis uses a logarithmic scale ranging from about10⁻⁶ to about 10⁻¹² V/m. In an ideal noiseless environment, the datawould follow a smooth curve. As can be seen from FIG. 11A, the datacontains a fair amount of noise, especially below 184.8 days and above185.1 days.

The vertical axis of the phase chart in FIG. 11B is the cosine of thephase of the collected data. In an ideal noiseless environment, the datawould be smoothly distributed from −1 to 1. As can be seen from FIG.11B, the data contains a fair amount of noise, especially below 184.8days and above 185.1 days.

FIG. 12 shows the difference between the phase of the signal measured atone of the frequencies of interest, 0.0625 Hz, and the phase of thesignal measured at three of the frequencies where little or no Signal isexpected, 0.03125 Hz (FIG. 12A), 0.09375 Hz (FIG. 12B), and 0.15625 Hz(FIG. 12C), over the range of offsets.

A range of offsets was selected in which the difference in phase issmall, which means that the noise at the frequency of interest should bereadily modeled from the noise at frequencies where little or no Signalis expected. In the example shown in FIGS. 11-15, the data in the rangefrom 184.5-184.6 was chosen to estimate the noise.

FIG. 13 shows the CSEM signal after noise suppression. Comparing FIG. 13to FIG. 11, it can be seen that the noise level has dropped in both theamplitude chart (FIG. 13A) and in the phase chart (FIG. 13B). Thereduction in noise is illustrated in FIGS. 14 and 15, which combine thechart of the signal before noise suppression and the chart of the signalafter noise suppression. In FIG. 14, the data below 184.65 Julian days,where line 1405 is located, are the original data. The data above 184.65Julian days are the data after the noise suppression technique has beenapplied. The reduction in noise is apparent from the reduction in theaverage amplitude in FIG. 14A. FIG. 14B shows the corresponding phasedata.

In FIG. 15, the data above 185.15 Julian days, where line 1505 arelocated, is the original data. The data below 185.15 Julian days are thedata after the noise suppression technique has been applied. Again, thereduction in noise is apparent from the reduction in the averageamplitude in FIG. 15A. The corresponding phase data is shown in FIG.15B.

While the present invention has been described with reference to anexemplary embodiment thereof, those skilled in the art will know ofvarious changes in form that may be made without departing from thespirit and scope of the claimed invention as defined in the appendedclaims. For example, the person skilled in the art will recognize thatdifferent techniques for modeling the noise, other than that shown inEquations 1 and 2, could be used. As another example, the person skilledin the art will recognize that the transducer 105 might be replaced witha magnetic dipole, that the antenna 215 might be replaced with amagnetic antenna, or that both transducer 105 and antenna 215 might bereplaced with magnetic devices. All such variations will be deemedincluded in the following claims.

1. A method for improving the signal-to-noise ratio of a signal S(t), S(t) containing Signal and noise, the method comprising: (a) transforming measurements of S(t) to frequency domain, and obtaining a measurement of S(t) at a frequency-of-interest; (b) obtaining noise measurements of S(t) at one or more noise frequencies where the Signal portion of S(t) is expected to be small; wherein said one or more noise frequencies are also selected such that they will readily model the noise at the frequency-of-interest or because they are close to the frequency-of-interest, or both; (c) estimating the noise at the frequency-of-interest using the noise measurements at the one or more noise frequencies; and (d) subtracting the estimated noise from the measurement of S(t) at the frequency-of-interest.
 2. The method of claim 1 further comprising: repeating (a), (b), (c) and (d).
 3. The method of claim 1 where obtaining noise measurements of S(t) at the one or more noise frequencies comprises: obtaining measurements of S(t) at a time when the Signal portion of S(t) is expected to be small.
 4. The method of claim 1, where: obtaining a measurement of S(t) at the frequency-of-interest comprises obtaining measurements of the complex amplitude of S(t) at the frequency-of-interest; obtaining noise measurements of S(t) at the one or more noise frequencies comprises obtaining measurements of the complex amplitude of S(t) at the plurality of noise frequencies; estimating the noise comprises estimating the complex amplitude of the noise at the frequency-of-interest using the complex amplitudes of S(t) obtained at the one or more noise frequencies; and subtracting the estimated noise comprises subtracting the complex amplitude of the estimated noise at the frequency-of-interest from the complex amplitude of S(t) obtained at the frequency-of-interest.
 5. The method of claim 1 further comprising: generating a CSEM signal having a large amount of energy at the frequency-of-interest and small amount of energy at a plurality of low-signal frequencies; transmitting the CSEM signal; and receiving the signal S(t).
 6. The method of claim 5 further comprising: selecting a frequency for the CSEM signal.
 7. The method of claim 5 where generating the CSEM signal comprises: generating a CSEM signal in which the energy of the CSEM signal is concentrated into temporal frequencies suited to distinguish hydrocarbon reservoirs.
 8. The method of claim 5 further comprising: selecting the noise frequencies to coincide with a subset of the low-signal frequencies.
 9. The method of claim 5 further comprising: selecting the noise frequencies to avoid frequency components of the transmitted CSEM signal.
 10. The method of claim 5 where generating a CSEM signal comprises: generating a square wave.
 11. The method of claim 5 where generating a CSEM signal comprises: generating a tripeak wave.
 12. A computer program product, comprising a tangible non-transitory computer usable medium having a computer readable program code embodied therein, said computer readable program code adapted to be executed on a computer to implement a method for improving the signal-to-noise ratio of a signal S(t), S(t) containing Signal and noise, said method comprising: (a) transforming measurements of S(t) to frequency domain, and obtain a measurement of S(t) at a frequency-of-interest; (b) obtaining noise measurements of S(t) at one or more noise frequencies where the Signal portion of S(t) is expected to be small; wherein said one or more noise frequencies are also selected such that they will readily model the noise at the frequency-of-interest or because they are close to the frequency-of-interest, or both; (c) estimating the noise at the frequency-of-interest using the noise measurements at the one or more noise frequencies; and (d) subtracting the estimated noise from the measurement of S(t) at the frequency-of-interest.
 13. The computer program of claim 12 where the program further comprises executable instructions that cause the computer to: repeat (a), (b), (c) and (d).
 14. The computer program of claim 12 where, when obtaining noise measurements of S(t) at the one or more noise frequencies, the computer: obtains measurements of S(t) at time when the Signal portion of S(t) is expected to be small.
 15. The computer program of claim 12 where the measurements comprise data, the data comprises offset, amplitude and phase, and, when estimating the noise, the computer: sorts the data into bins, each bin being associated with a respective range of offsets; transforms the data in each bin into the frequency domain; selects from each bin data associated with the frequency-of-interest; selects from each bin data associated with the one or more noise frequencies; estimates, for each bin, a frequency-of-interest noise from the selected noise frequency data; and subtracts, on a bin-by-bin basis, the estimated frequency-of-interest noise from the data associated with the frequency-of-interest.
 16. The computer program of claim 12, where: when obtaining a measurement of S(t) at the frequency-of-interest, the computer obtains measurements of the complex amplitude of S(t) at the frequency-of-interest; when obtaining noise measurements of S(t) at the one or more noise frequencies, the computer obtains measurements of the complex amplitude of S(t) at the one or more noise frequencies; when estimating the noise, the computer estimates the complex amplitude of the noise at the frequency-of-interest using the complex amplitudes of S(t) obtained at the one or more noise frequencies; and when subtracting the estimated noise comprises, the computer subtracts the complex amplitude of the estimated noise at the frequency-of-interest from the complex amplitude of S(t) obtained at the frequency-of-interest.
 17. The computer program of claim 12, the program further comprising executable instructions that cause the computer to: generate a CSEM signal having a large amount of energy at the frequency-of-interest and small amount of energy at a plurality of low-signal frequencies; transmit the CSEM signal; and receive the signal S(t).
 18. The computer program of claim 17, the program further comprising executable instructions that cause the computer to: select a frequency for the CSEM signal.
 19. The computer program of claim 17 where, when generating a CSEM signal, the computer: generates a CSEM signal in which the energy of the CSEM signal is concentrated into temporal frequencies suited to distinguishing hydrocarbon reservoirs.
 20. The computer program of claim 17, the program further comprising executable instructions that cause the computer to: select the noise frequencies to coincide with a subset of the low-signal frequencies.
 21. The computer program of claim 17, the program further comprising executable instructions that cause the computer to: select the noise frequencies to avoid frequency components of the transmitted CSEM signal.
 22. The computer program of claim 17 where, when generating a CSEM signal, the computer: generates a square wave.
 23. The computer program of claim 17 where, when generating a CSEM signal, the computer: generates a tripeak wave.
 24. A method for improving the signal-to-noise ratio of a transmitted CSEM signal S(t), S(t) containing Signal and noise, the method comprising: (a) selecting an S(t) having a large amount of energy at the frequency-of-interest and small amount of energy at a plurality of low-signal frequencies; (b) transforming measurements of S(t) to frequency domain, and obtaining a measurement of S(t) at a frequency-of-interest; (c) obtaining noise measurements of S(t) at one or more noise frequencies where the Signal portion of S(t) is expected to be small; (d) estimating the noise at the frequency-of-interest using the noise measurements at the one or more noise frequencies; and (e) subtracting the estimated noise from the measurement of S(t) at the frequency-of-interest.
 25. The method of claim 24, further comprising: selecting the noise frequencies to coincide with a subset of the low-signal frequencies, said subset being selected to avoid frequency components of the transmitted CSEM signal. 